During a prison visit with his sister, Dzhokhar Tsarnaev, the accused Boston Marathon bomber, made a damaging statement that was overheard by an FBI agent, federal prosecutors said today in a court filing.

The filing said that Tsarnaev, despite the presence of the agent, who was legally allowed in the room, “was unable to temper his remarks and made a statement to his detriment which was overheard by the agent.”

The filing did not say what the statement was.

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The filing was made as part of an ongoing battle between the prosecution and defense over special administrative measures, special prison restrictions, that have been imposed on Tsarnaev.

The defense alleged in a court filing last week that the FBI has been monitoring their preparation for the case and that the US Bureau of Prisons has attempted to screen digital documents that the defense team has brought to prison to review with Tsarnaev, in violation of his constitutional rights to mount his case without government interference.

Tsarnaev, 20, faces federal charges that could bring him the death penalty in the April 15 terror bombings that killed three people and wounded more than 260 others. He also faces state charges in the death of an MIT police officer several days later. He is currently being held without bail at a federal prison facility in Devens.

In the filing today, the prosecutors said the FBI agent was legally permitted to be in the room under the special restrictions.

“As such, his observations ... were permissible. The defense provides no support for the contention that the agent was required to close himself off from the conversation. There was no expectation of privacy on the party [sic] of Tsarnaev, his visitors, or the investigator.”

Prosecutors disclosed in the filing that Tsarnaev’s attorneys requested in December that Tsarnaev be able to meet with each of his sisters. Since then, Tsarnaev has received two social visits. Such non-legal visits are restricted to one immediate family member under the special restrictions, prosecutors said.

The defense also asked that an investigator from the federal public defender’s office be able to attend the visits. During the second visit, the investigator started to explain the rationale behind the special restrictions to Tsarnaev’s sister, prosecutors said.

Tsarnaev made the damaging statement that was overheard by the FBI agent “in response to [the investigator’s] comment regarding the prohibition against providing information to third parties outside of the prison,” prosecutors said.

Prosecutors also said that the Bureau of Prisons, under the special restrictions, reviews all materials that are brought into a BOP facility. Prosecutors said the review is a “cursory one and does not involve a detailed review of the material.”

“With respect to digital media, the review is to determine whether or not the item contains any viruses. The review has never been substantive,” prosecutors said.

Prosecutors said that on Jan. 24, the defense brought a disk to the prison that had not been reviewed. A BOP official asked to review the disk. When the defense refused to allow it to be reviewed, it was not given to Tsarnaev.

“If the defense chooses not to comply with [the special restrictions], the material will not be provided to the defendant. That is the choice of the defense,” prosecutors said.

Tsarnaev allegedly acted in concert with his older brother, Tamerlan, 26, who was killed in a violent confrontation with police as the two brothers tried to flee the area several days after the bombing.

The bombings, which struck at the heart of what is normally a colorful, joyful athletic spectacle, shook the nation, raising the specter of terrorism again on American soil.